The shared mailbox should populate under your main mailbox (left panel).

How to send as shared mailbox in Microsoft Office 2010:

Open a new Mail Message

Click the From button

Select Other E-Mail Address

Type in the Shared E-Mail Address in the From field

Send message

If you do not have Send As permissions for the shared mailbox, Exchange will not allow you to send.

In some cases when you have Send As permission, you may see the error message "You don't have permission to send to: <destination email address>". That is a known issue with Outlook, there is no ETA for a fix. The message can be ignored.